How do you find the exact value #tan(x-y)# if #sinx=8/17,cosy=3/5#?

Question

17070 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2016-12-04T10:37:03

The answer is #=-36/77#

We use

#cos^2x+sin^2x=1#

#cos^2y+sin^2y=1#

#sin(x-y)=sinxcosy-sinycosx#

#cos(x-y)=cosxcosy+sinxsiny#

#sinx=8/17#

#cosx=sqrt(1-sin^2x)=sqrt(1-64/289)=sqrt(225/289)=15/17#

#cosy=3/5#

#siny=sqrt(1-cos^2y)=sqrt(1-9/25)=sqrt(16/25)=4/5#

#tan(x-y)=sin(x-y)/cos(x-y)#

#=(sinxcosy-sinycosx)/(cosxcosy+sinxsiny)#

#=(8/17*3/5-4/5*15/17)/(15/17*3/5+8/17*4/5)#

#=(24/85-60/85)/(45/85+32/85)#

#=-36/77#